Reinvestigation of Single-Phase FLLs

Besides well-known phase-locked loops, frequency-locked loops (FLLs) are applicable to grid synchronization for grid-tied power converters. The models, principles, and algorithm structures of existing notch filter-based single-phase FLLs are often described with different theories in previous studies. Consequently, a theoretically unified understanding and further advancements of such type of FLLs are restricted. This paper reinvestigates notch filter-based single-phase FLLs and develops a generalized design framework for such types of FLLs. The model derivations of the FLLs are made uniformly via the Popov’s model reference adaptive control theory, in order to achieve the theoretically unified understanding. Three major contributions are received in this paper. First, a family of FLLs is derived, and existing seemingly different FLL designs are accordingly developed into a family of homologous FLLs. Second, the performance differences between the FLLs in the whole family are evaluated and compared quantitatively from the algorithm structure point of view, in terms of stability, convergence speed, and harmonic suppression capability. Finally, an enhanced single-phase FLL (named the $1\phi $ -EFLL) is recommended by the family of the homologous FLLs. The designs and the performance evaluations are verified by both simulations and experiments.